Question

A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for π, and round your answer to the nearest hundredth. 38.47 units2 94.99 units2 153.86 units2 379.94 units2

Answer 1

Answer:

Answer choice A) About 38.47 square units

Step-by-step explanation:

Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:

$\dfrac{22}{2\pi}\approx 3.503$

Since the area of a circle is $\pi r^2$, the area of this circle is:

$\pi \cdot 3.503^2= 3.14\cdot 12.271\approx 38.47$

Hope this helps!